Answer:8x+2
Step-by-step explanation:
Area is length times width. Therefore, width is area divided by length. Convert 11 7/8 to the improper fraction 95/8 and convert 4 3/4 to 19/4. Then, you can fine 95/8 divided by 19/4 by flipping the second fraction and multiplying so that you have 95/8 times 4/19. 4 times 95 is 380 and 8 times 19 is 152. Therefore, the answer is 380/152. This is equivalent to 5/2 or 2.5.
I think this question is a part of another question; you can have any ratio that can add up to 114 cm.
Looks like you have most of the details already, but you're missing one crucial piece.
is parameterized by
![\vec r(u,v)=\langle u\cos3v,u\sin3v,v\rangle](https://tex.z-dn.net/?f=%5Cvec%20r%28u%2Cv%29%3D%5Clangle%20u%5Ccos3v%2Cu%5Csin3v%2Cv%5Crangle)
for
and
, and a normal vector to this surface is
![\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\left\langle\sin3v,-\cos3v,3u\right\rangle](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%5Cvec%20r%7D%7B%5Cpartial%20u%7D%5Ctimes%5Cdfrac%7B%5Cpartial%5Cvec%20r%7D%7B%5Cpartial%20v%7D%3D%5Cleft%5Clangle%5Csin3v%2C-%5Ccos3v%2C3u%5Cright%5Crangle)
with norm
![\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|=\sqrt{\sin^23v+(-\cos3v)^2+(3u)^2}=\sqrt{9u^2+1}](https://tex.z-dn.net/?f=%5Cleft%5C%7C%5Cdfrac%7B%5Cpartial%5Cvec%20r%7D%7B%5Cpartial%20u%7D%5Ctimes%5Cdfrac%7B%5Cpartial%5Cvec%20r%7D%7B%5Cpartial%20v%7D%5Cright%5C%7C%3D%5Csqrt%7B%5Csin%5E23v%2B%28-%5Ccos3v%29%5E2%2B%283u%29%5E2%7D%3D%5Csqrt%7B9u%5E2%2B1%7D)
So the integral of
is
![\displaystyle\iint_\sigma f(x,y,z)\,\mathrm dA=\boxed{\int_0^{2\pi/3}\int_0^7(u^2+v^2)\sqrt{9u^2+1}\,\mathrm du\,\mathrm dv}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_%5Csigma%20f%28x%2Cy%2Cz%29%5C%2C%5Cmathrm%20dA%3D%5Cboxed%7B%5Cint_0%5E%7B2%5Cpi%2F3%7D%5Cint_0%5E7%28u%5E2%2Bv%5E2%29%5Csqrt%7B9u%5E2%2B1%7D%5C%2C%5Cmathrm%20du%5C%2C%5Cmathrm%20dv%7D)